Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1104,2,Mod(47,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1104.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.81548438315\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3814238552064.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} - 4x^{5} - 12x^{3} + 9x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.4 | ||
Root | \(-0.696260 - 1.58595i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1104.47 |
Dual form | 1104.2.e.f.47.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1104\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(277\) | \(415\) | \(737\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.696260 | + | 1.58595i | −0.401986 | + | 0.915646i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.04950i | 0.916565i | 0.888807 | + | 0.458283i | \(0.151535\pi\) | ||||
−0.888807 | + | 0.458283i | \(0.848465\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.04950i | 0.774639i | 0.921946 | + | 0.387319i | \(0.126599\pi\) | ||||
−0.921946 | + | 0.387319i | \(0.873401\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.03044 | − | 2.20846i | −0.676815 | − | 0.736154i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.66837 | −0.804543 | −0.402271 | − | 0.915520i | \(-0.631779\pi\) | ||||
−0.402271 | + | 0.915520i | \(0.631779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.30873 | −1.47238 | −0.736189 | − | 0.676776i | \(-0.763377\pi\) | ||||
−0.736189 | + | 0.676776i | \(0.763377\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.25040 | − | 1.42699i | −0.839249 | − | 0.368446i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.71077i | − | 1.62760i | −0.581144 | − | 0.813801i | \(-0.697395\pi\) | ||
0.581144 | − | 0.813801i | \(-0.302605\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.878038i | 0.201436i | 0.994915 | + | 0.100718i | \(0.0321139\pi\) | ||||
−0.994915 | + | 0.100718i | \(0.967886\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.25040 | − | 1.42699i | −0.709295 | − | 0.311394i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.799541 | 0.159908 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.91621 | − | 1.68251i | 0.946126 | − | 0.323799i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.68294i | − | 0.683904i | −0.939717 | − | 0.341952i | \(-0.888912\pi\) | ||
0.939717 | − | 0.341952i | \(-0.111088\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.90588i | 0.701516i | 0.936466 | + | 0.350758i | \(0.114076\pi\) | ||||
−0.936466 | + | 0.350758i | \(0.885924\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.85788 | − | 4.23188i | 0.323415 | − | 0.736676i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.20046 | −0.710007 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.668367 | −0.109879 | −0.0549394 | − | 0.998490i | \(-0.517497\pi\) | ||||
−0.0549394 | + | 0.998490i | \(0.517497\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.69626 | − | 8.41936i | 0.591875 | − | 1.34818i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.92686i | − | 0.300925i | −0.988616 | − | 0.150462i | \(-0.951924\pi\) | ||
0.988616 | − | 0.150462i | \(-0.0480763\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.63831i | 1.46983i | 0.678160 | + | 0.734915i | \(0.262778\pi\) | ||||
−0.678160 | + | 0.734915i | \(0.737222\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.52624 | − | 4.16140i | 0.674733 | − | 0.620345i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.97710 | 0.871850 | 0.435925 | − | 0.899983i | \(-0.356421\pi\) | ||||
0.435925 | + | 0.899983i | \(0.356421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.79954 | 0.399934 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.6429 | + | 4.67244i | 1.49031 | + | 0.654273i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.878038i | 0.120608i | 0.998180 | + | 0.0603039i | \(0.0192070\pi\) | ||||
−0.998180 | + | 0.0603039i | \(0.980793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.46882i | − | 0.737416i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.39252 | − | 0.611343i | −0.184444 | − | 0.0809743i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.4170 | −1.87693 | −0.938467 | − | 0.345368i | \(-0.887754\pi\) | ||||
−0.938467 | + | 0.345368i | \(0.887754\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.33673 | −0.427225 | −0.213613 | − | 0.976918i | \(-0.568523\pi\) | ||||
−0.213613 | + | 0.976918i | \(0.568523\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.52624 | − | 4.16140i | 0.570253 | − | 0.524287i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.8803i | − | 1.34953i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.5659i | − | 1.53516i | −0.640951 | − | 0.767582i | \(-0.721460\pi\) | ||
0.640951 | − | 0.767582i | \(-0.278540\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.696260 | − | 1.58595i | 0.0838199 | − | 0.190925i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.43991 | −1.00163 | −0.500816 | − | 0.865554i | \(-0.666967\pi\) | ||||
−0.500816 | + | 0.865554i | \(0.666967\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.84593 | −1.03534 | −0.517669 | − | 0.855581i | \(-0.673200\pi\) | ||||
−0.517669 | + | 0.855581i | \(0.673200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.556688 | + | 1.26803i | −0.0642809 | + | 0.146419i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.46882i | − | 0.623230i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.22097i | 0.362387i | 0.983447 | + | 0.181194i | \(0.0579960\pi\) | ||||
−0.983447 | + | 0.181194i | \(0.942004\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.754597 | + | 8.96831i | −0.0838441 | + | 0.996479i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.28584 | 1.01925 | 0.509626 | − | 0.860396i | \(-0.329784\pi\) | ||||
0.509626 | + | 0.860396i | \(0.329784\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.7537 | 1.49180 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.84093 | + | 2.56428i | 0.626214 | + | 0.274920i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.7373i | − | 1.45615i | −0.685496 | − | 0.728076i | \(-0.740415\pi\) | ||
0.685496 | − | 0.728076i | \(-0.259585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10.8803i | − | 1.14056i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.19451 | − | 2.71951i | −0.642340 | − | 0.282000i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.79954 | −0.184629 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.2858 | −1.14590 | −0.572952 | − | 0.819589i | \(-0.694202\pi\) | ||||
−0.572952 | + | 0.819589i | \(0.694202\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.41797 | + | 5.89298i | 0.544526 | + | 0.592267i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.70880i | 0.966062i | 0.875603 | + | 0.483031i | \(0.160464\pi\) | ||||
−0.875603 | + | 0.483031i | \(0.839536\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.10098i | − | 0.108483i | −0.998528 | − | 0.0542413i | \(-0.982726\pi\) | ||
0.998528 | − | 0.0542413i | \(-0.0172740\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.92461 | − | 6.66170i | 0.285413 | − | 0.650115i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.6175 | −1.79982 | −0.899909 | − | 0.436077i | \(-0.856368\pi\) | ||||
−0.899909 | + | 0.436077i | \(0.856368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.2166 | −1.17013 | −0.585067 | − | 0.810985i | \(-0.698932\pi\) | ||||
−0.585067 | + | 0.810985i | \(0.698932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.465357 | − | 1.05999i | 0.0441698 | − | 0.100610i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.56029i | − | 0.334924i | −0.985879 | − | 0.167462i | \(-0.946443\pi\) | ||
0.985879 | − | 0.167462i | \(-0.0535572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.04950i | − | 0.191117i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.7791 | + | 11.7241i | 0.996527 | + | 1.08390i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.7537 | 1.26080 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.87982 | −0.352711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.05589 | + | 1.34160i | 0.275541 | + | 0.120968i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8862i | 1.06313i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.9576i | − | 1.41601i | −0.706208 | − | 0.708004i | \(-0.749596\pi\) | ||
0.706208 | − | 0.708004i | \(-0.250404\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.2858 | − | 6.71077i | −1.34584 | − | 0.590851i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.56009 | −0.311047 | −0.155523 | − | 0.987832i | \(-0.549706\pi\) | ||||
−0.155523 | + | 0.987832i | \(0.549706\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.79954 | −0.156040 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.44831 | + | 10.0758i | 0.296783 | + | 0.867186i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.07468i | 0.604431i | 0.953240 | + | 0.302216i | \(0.0977262\pi\) | ||||
−0.953240 | + | 0.302216i | \(0.902274\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.51567i | 0.807109i | 0.914956 | + | 0.403554i | \(0.132225\pi\) | ||||
−0.914956 | + | 0.403554i | \(0.867775\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.16162 | + | 9.47936i | −0.350471 | + | 0.798306i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.1657 | 1.18459 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.54818 | 0.626843 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.94921 | + | 4.43992i | −0.160768 | + | 0.366198i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.5435i | 1.02760i | 0.857909 | + | 0.513802i | \(0.171763\pi\) | ||||
−0.857909 | + | 0.513802i | \(0.828237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00488i | 0.651428i | 0.945468 | + | 0.325714i | \(0.105605\pi\) | ||||
−0.945468 | + | 0.325714i | \(0.894395\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.8205 | + | 13.6258i | −1.19816 | + | 1.10158i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00510 | −0.642985 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9542 | 1.11367 | 0.556833 | − | 0.830624i | \(-0.312016\pi\) | ||||
0.556833 | + | 0.830624i | \(0.312016\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.39252 | − | 0.611343i | −0.110434 | − | 0.0484826i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.04950i | − | 0.161523i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.438414i | − | 0.0343392i | −0.999853 | − | 0.0171696i | \(-0.994534\pi\) | ||
0.999853 | − | 0.0171696i | \(-0.00546553\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.67325 | + | 3.80772i | 0.675212 | + | 0.296431i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.28073 | −0.563400 | −0.281700 | − | 0.959503i | \(-0.590898\pi\) | ||||
−0.281700 | + | 0.959503i | \(0.590898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.1827 | 1.16790 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.93911 | − | 1.78281i | 0.148288 | − | 0.136335i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 11.9108i | − | 0.905558i | −0.891623 | − | 0.452779i | \(-0.850433\pi\) | ||
0.891623 | − | 0.452779i | \(-0.149567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.63866i | 0.123871i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0380 | − | 22.8646i | 0.754501 | − | 1.71861i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.5762 | −1.61268 | −0.806340 | − | 0.591453i | \(-0.798555\pi\) | ||||
−0.806340 | + | 0.591453i | \(0.798555\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.2400 | 1.43010 | 0.715050 | − | 0.699073i | \(-0.246404\pi\) | ||||
0.715050 | + | 0.699073i | \(0.246404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.32324 | − | 5.29188i | 0.171738 | − | 0.391187i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.36982i | − | 0.100711i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.9068i | 1.30948i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.44831 | + | 10.0758i | 0.250827 | + | 0.732906i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.5768 | −1.92303 | −0.961514 | − | 0.274756i | \(-0.911403\pi\) | ||||
−0.961514 | + | 0.274756i | \(0.911403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.64547 | −0.478351 | −0.239176 | − | 0.970976i | \(-0.576877\pi\) | ||||
−0.239176 | + | 0.970976i | \(0.576877\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.2555 | + | 7.57549i | 1.23569 | + | 0.542492i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.3484i | 1.09353i | 0.837287 | + | 0.546764i | \(0.184141\pi\) | ||||
−0.837287 | + | 0.546764i | \(0.815859\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.21736i | − | 0.0862967i | −0.999069 | − | 0.0431483i | \(-0.986261\pi\) | ||
0.999069 | − | 0.0431483i | \(-0.0137388\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.9288 | + | 8.74910i | 1.40567 | + | 0.617114i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.54818 | 0.529779 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.94910 | 0.275817 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.03044 | + | 2.20846i | 0.141126 | + | 0.153499i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.34293i | − | 0.162064i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.2957i | − | 0.708782i | −0.935097 | − | 0.354391i | \(-0.884688\pi\) | ||
0.935097 | − | 0.354391i | \(-0.115312\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.87637 | − | 13.3852i | 0.402642 | − | 0.917141i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.7537 | −1.34719 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00510 | −0.543422 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.15907 | − | 14.0292i | 0.416191 | − | 0.948003i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.6257i | 2.39644i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.19801i | 0.548979i | 0.961590 | + | 0.274490i | \(0.0885089\pi\) | ||||
−0.961590 | + | 0.274490i | \(0.911491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.62342 | − | 1.76575i | −0.108228 | − | 0.117717i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.3602 | 1.08587 | 0.542933 | − | 0.839776i | \(-0.317314\pi\) | ||||
0.542933 | + | 0.839776i | \(0.317314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0286 | 1.12528 | 0.562640 | − | 0.826702i | \(-0.309786\pi\) | ||||
0.562640 | + | 0.826702i | \(0.309786\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.67325 | + | 3.80772i | 0.570658 | + | 0.250530i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.92686i | 0.126233i | 0.998006 | + | 0.0631164i | \(0.0201039\pi\) | ||||
−0.998006 | + | 0.0631164i | \(0.979896\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.2501i | 0.799107i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.10828 | − | 2.24263i | −0.331818 | − | 0.145674i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.3941 | −0.931078 | −0.465539 | − | 0.885027i | \(-0.654139\pi\) | ||||
−0.465539 | + | 0.885027i | \(0.654139\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0051 | −0.644485 | −0.322243 | − | 0.946657i | \(-0.604437\pi\) | ||||
−0.322243 | + | 0.946657i | \(0.604437\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.6979 | − | 7.44103i | −0.878718 | − | 0.477342i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.73767i | 0.366566i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.66127i | − | 0.296590i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.46536 | + | 14.7268i | −0.409725 | + | 0.933275i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.9491 | −1.00670 | −0.503349 | − | 0.864083i | \(-0.667899\pi\) | ||||
−0.503349 | + | 0.864083i | \(0.667899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.66837 | 0.167759 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.57618 | + | 21.8127i | −0.599684 | + | 1.36596i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.3039i | 1.70317i | 0.524219 | + | 0.851584i | \(0.324357\pi\) | ||||
−0.524219 | + | 0.851584i | \(0.675643\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.36982i | − | 0.0851165i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.13362 | + | 7.47799i | −0.503458 | + | 0.462876i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.61747 | −0.408051 | −0.204025 | − | 0.978966i | \(-0.565402\pi\) | ||||
−0.204025 | + | 0.978966i | \(0.565402\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.79954 | −0.110545 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.7866 | + | 9.56475i | 1.33332 | + | 0.585353i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.170783i | 0.0104128i | 0.999986 | + | 0.00520641i | \(0.00165726\pi\) | ||||
−0.999986 | + | 0.00520641i | \(0.998343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.9854i | 1.76074i | 0.474288 | + | 0.880370i | \(0.342705\pi\) | ||||
−0.474288 | + | 0.880370i | \(0.657295\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.2555 | + | 7.57549i | 1.04435 | + | 0.458490i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.13347 | −0.128653 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2010 | 1.15368 | 0.576840 | − | 0.816857i | \(-0.304286\pi\) | ||||
0.576840 | + | 0.816857i | \(0.304286\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.62597 | − | 7.93066i | 0.516424 | − | 0.474796i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.71077i | 0.400331i | 0.979762 | + | 0.200166i | \(0.0641480\pi\) | ||||
−0.979762 | + | 0.200166i | \(0.935852\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 25.9874i | − | 1.54479i | −0.635142 | − | 0.772395i | \(-0.719058\pi\) | ||
0.635142 | − | 0.772395i | \(-0.280942\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.25295 | − | 2.85397i | 0.0742183 | − | 0.169055i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.94910 | 0.233108 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28.0345 | −1.64909 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.85788 | − | 17.8987i | 0.460637 | − | 1.04924i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.29539i | − | 0.426201i | −0.977030 | − | 0.213100i | \(-0.931644\pi\) | ||
0.977030 | − | 0.213100i | \(-0.0683562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 29.5477i | − | 1.72033i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.1183 | + | 4.48955i | −0.761199 | + | 0.260510i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.30873 | 0.307012 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.7537 | −1.13859 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.3976 | − | 6.75985i | −0.884570 | − | 0.388343i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6.83864i | − | 0.391580i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.7455i | − | 1.41230i | −0.708064 | − | 0.706149i | \(-0.750431\pi\) | ||
0.708064 | − | 0.706149i | \(-0.249569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.74609 | + | 0.766568i | 0.0993317 | + | 0.0436085i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.2394 | 0.920855 | 0.460427 | − | 0.887697i | \(-0.347696\pi\) | ||||
0.460427 | + | 0.887697i | \(0.347696\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2807 | 0.863718 | 0.431859 | − | 0.901941i | \(-0.357858\pi\) | ||||
0.431859 | + | 0.901941i | \(0.357858\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.52880 | + | 9.27655i | 0.480543 | + | 0.522674i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1507i | 0.907115i | 0.891227 | + | 0.453558i | \(0.149845\pi\) | ||||
−0.891227 | + | 0.453558i | \(0.850155\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.82742i | 0.550230i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.9626 | − | 29.5263i | 0.723502 | − | 1.64800i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.89231 | 0.327857 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.24455 | −0.235445 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.50590 | − | 19.3748i | 0.470377 | − | 1.07143i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.2501i | 0.675369i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.4795i | 1.95013i | 0.221918 | + | 0.975065i | \(0.428768\pi\) | ||||
−0.221918 | + | 0.975065i | \(0.571232\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.35708 | + | 1.47606i | 0.0743676 | + | 0.0808877i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.7537 | 1.40708 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.54308 | 0.519845 | 0.259922 | − | 0.965630i | \(-0.416303\pi\) | ||||
0.259922 | + | 0.965630i | \(0.416303\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.64643 | + | 2.47889i | 0.306672 | + | 0.134635i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 10.4223i | − | 0.564400i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0842i | 1.08444i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.25040 | + | 1.42699i | 0.174996 | + | 0.0768264i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.5098 | 1.31575 | 0.657877 | − | 0.753125i | \(-0.271455\pi\) | ||||
0.657877 | + | 0.753125i | \(0.271455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.6639 | −1.15964 | −0.579820 | − | 0.814745i | \(-0.696877\pi\) | ||||
−0.579820 | + | 0.814745i | \(0.696877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.0989 | + | 8.93199i | −1.39305 | + | 0.476755i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 28.5694i | − | 1.52059i | −0.649576 | − | 0.760297i | \(-0.725054\pi\) | ||
0.649576 | − | 0.760297i | \(-0.274946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 17.2976i | − | 0.918062i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.57618 | + | 21.8127i | −0.506825 | + | 1.15445i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.0457966 | −0.00241705 | −0.00120853 | − | 0.999999i | \(-0.500385\pi\) | ||||
−0.00120853 | + | 0.999999i | \(0.500385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.2290 | 0.959424 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.70136 | − | 6.15318i | 0.141785 | − | 0.322958i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 18.1297i | − | 0.948954i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.9860i | − | 1.25206i | −0.779799 | − | 0.626031i | \(-0.784679\pi\) | ||
0.779799 | − | 0.626031i | \(-0.215321\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.25539 | + | 3.91238i | −0.221527 | + | 0.203670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.79954 | −0.0934275 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.2400 | −1.61755 | −0.808774 | − | 0.588120i | \(-0.799868\pi\) | ||||
−0.808774 | + | 0.588120i | \(0.799868\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.8508 | − | 8.27587i | −0.973452 | − | 0.427364i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.5517i | 1.00697i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.21282i | − | 0.113665i | −0.998384 | − | 0.0568324i | \(-0.981900\pi\) | ||
0.998384 | − | 0.0568324i | \(-0.0181001\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.3079 | + | 11.1106i | 1.29656 | + | 0.569215i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.2084 | 0.571231 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.2858 | − | 19.5701i | 1.08202 | − | 0.994802i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 39.0100i | 1.97789i | 0.148298 | + | 0.988943i | \(0.452620\pi\) | ||||
−0.148298 | + | 0.988943i | \(0.547380\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.71077i | 0.339378i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.47875 | − | 5.64611i | 0.125036 | − | 0.284809i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.60138 | −0.332151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3992 | 1.52569 | 0.762846 | − | 0.646580i | \(-0.223801\pi\) | ||||
0.762846 | + | 0.646580i | \(0.223801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.25295 | − | 2.85397i | 0.0627259 | − | 0.142877i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.09703i | 0.354409i | 0.984174 | + | 0.177204i | \(0.0567054\pi\) | ||||
−0.984174 | + | 0.177204i | \(0.943295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.7353i | − | 1.03290i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.3806 | − | 1.54655i | −0.913338 | − | 0.0768486i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.78345 | 0.0884023 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.76565 | −0.285093 | −0.142547 | − | 0.989788i | \(-0.545529\pi\) | ||||
−0.142547 | + | 0.989788i | \(0.545529\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.2201 | − | 4.92582i | −0.553445 | − | 0.242973i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 29.5477i | − | 1.45395i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.0313i | 0.934212i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.0913 | − | 6.62538i | −0.739026 | − | 0.324446i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.86143 | −0.0909368 | −0.0454684 | − | 0.998966i | \(-0.514478\pi\) | ||||
−0.0454684 | + | 0.998966i | \(0.514478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.8849 | −0.725447 | −0.362723 | − | 0.931897i | \(-0.618153\pi\) | ||||
−0.362723 | + | 0.931897i | \(0.618153\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1362 | − | 13.2002i | −0.590081 | − | 0.641815i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.36554i | − | 0.260267i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.83864i | − | 0.330945i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.86298 | + | 22.4659i | −0.476189 | + | 1.08467i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.73765 | −0.0836998 | −0.0418499 | − | 0.999124i | \(-0.513325\pi\) | ||||
−0.0418499 | + | 0.999124i | \(0.513325\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.59398 | 0.461057 | 0.230529 | − | 0.973066i | \(-0.425954\pi\) | ||||
0.230529 | + | 0.973066i | \(0.425954\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.25550 | + | 11.9710i | −0.251982 | + | 0.573966i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.878038i | − | 0.0420023i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.4021i | 1.64192i | 0.570984 | + | 0.820961i | \(0.306562\pi\) | ||||
−0.570984 | + | 0.820961i | \(0.693438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.68431 | − | 6.18268i | −0.270681 | − | 0.294413i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.39411 | −0.113748 | −0.0568738 | − | 0.998381i | \(-0.518113\pi\) | ||||
−0.0568738 | + | 0.998381i | \(0.518113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.1547 | 1.33466 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.8933 | − | 8.73354i | −0.940922 | − | 0.413082i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.6156i | − | 1.30326i | −0.758537 | − | 0.651631i | \(-0.774085\pi\) | ||
0.758537 | − | 0.651631i | \(-0.225915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.14157i | 0.242107i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.6953 | − | 5.57348i | −0.596477 | − | 0.261865i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.2991 | 1.04540 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.8747 | −0.508698 | −0.254349 | − | 0.967113i | \(-0.581861\pi\) | ||||
−0.254349 | + | 0.967113i | \(0.581861\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.2909 | − | 32.9916i | −0.527016 | − | 1.53992i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 27.0586i | − | 1.26024i | −0.776497 | − | 0.630122i | \(-0.783005\pi\) | ||
0.776497 | − | 0.630122i | \(-0.216995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.8431i | 1.24750i | 0.781622 | + | 0.623752i | \(0.214393\pi\) | ||||
−0.781622 | + | 0.623752i | \(0.785607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.57363 | − | 12.6957i | 0.258471 | − | 0.588747i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.3551 | −0.941923 | −0.470961 | − | 0.882154i | \(-0.656093\pi\) | ||||
−0.470961 | + | 0.882154i | \(0.656093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.7537 | 1.18920 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.71576 | + | 22.1306i | −0.447678 | + | 1.01972i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25.7186i | − | 1.18254i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.702027i | 0.0322112i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.93911 | − | 1.78281i | 0.0887859 | − | 0.0816291i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.9217 | −0.864554 | −0.432277 | − | 0.901741i | \(-0.642290\pi\) | ||||
−0.432277 | + | 0.901741i | \(0.642290\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.54818 | 0.161783 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.25040 | + | 1.42699i | 0.147898 | + | 0.0649301i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 23.1303i | − | 1.05029i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.14980i | 0.0974167i | 0.998813 | + | 0.0487084i | \(0.0155105\pi\) | ||||
−0.998813 | + | 0.0487084i | \(0.984490\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.695301 | + | 0.305250i | 0.0314426 | + | 0.0138039i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7891 | −0.667425 | −0.333712 | − | 0.942675i | \(-0.608301\pi\) | ||||
−0.333712 | + | 0.942675i | \(0.608301\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.7153 | −1.11312 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.0777 | + | 11.1041i | −0.542851 | + | 0.499094i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 17.2976i | − | 0.775904i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6160i | 0.699070i | 0.936923 | + | 0.349535i | \(0.113660\pi\) | ||||
−0.936923 | + | 0.349535i | \(0.886340\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.06929 | − | 11.5468i | 0.226479 | − | 0.515875i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.0928 | 0.450015 | 0.225007 | − | 0.974357i | \(-0.427759\pi\) | ||||
0.225007 | + | 0.974357i | \(0.427759\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.8982 | −0.885458 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5711 | + | 24.0789i | −0.469478 | + | 1.06938i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 35.5981i | − | 1.57786i | −0.614483 | − | 0.788930i | \(-0.710635\pi\) | ||
0.614483 | − | 0.788930i | \(-0.289365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 18.1297i | − | 0.802013i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.47731 | + | 4.31662i | 0.0652247 | + | 0.190584i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.25646 | 0.0994314 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.9491 | −0.701441 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.8898 | + | 8.29298i | 0.829170 | + | 0.364022i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.6179i | 0.728045i | 0.931390 | + | 0.364022i | \(0.118597\pi\) | ||||
−0.931390 | + | 0.364022i | \(0.881403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.95606i | 0.304167i | 0.988368 | + | 0.152084i | \(0.0485983\pi\) | ||||
−0.988368 | + | 0.152084i | \(0.951402\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.59883 | − | 1.14093i | −0.113422 | − | 0.0497945i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.2114 | 1.14179 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.2729 | + | 31.8394i | 1.27034 | + | 1.38171i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.2292i | 0.443075i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 38.1565i | − | 1.64965i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.0226 | − | 34.2186i | 0.648275 | − | 1.47664i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.47020 | −0.321764 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.428918 | −0.0184406 | −0.00922031 | − | 0.999957i | \(-0.502935\pi\) | ||||
−0.00922031 | + | 0.999957i | \(0.502935\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.3961 | + | 30.5136i | −0.574880 | + | 1.30947i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 25.0378i | − | 1.07250i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.9889i | 1.49602i | 0.663688 | + | 0.748010i | \(0.268990\pi\) | ||||
−0.663688 | + | 0.748010i | \(0.731010\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.77505 | + | 7.36905i | 0.289152 | + | 0.314503i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.23376 | 0.137763 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.60138 | −0.280719 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.17246 | + | 0.953751i | 0.0922158 | + | 0.0404845i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.3944i | 0.482796i | 0.970426 | + | 0.241398i | \(0.0776059\pi\) | ||||
−0.970426 | + | 0.241398i | \(0.922394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 51.1672i | − | 2.16414i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.3992 | − | 12.4678i | −1.19902 | − | 0.526391i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.5075 | −1.15930 | −0.579651 | − | 0.814865i | \(-0.696811\pi\) | ||||
−0.579651 | + | 0.814865i | \(0.696811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.29683 | 0.306980 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.3806 | − | 1.54655i | −0.771911 | − | 0.0649489i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4.25146i | − | 0.178230i | −0.996021 | − | 0.0891152i | \(-0.971596\pi\) | ||
0.996021 | − | 0.0891152i | \(-0.0284039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.66461i | 0.153359i | 0.997056 | + | 0.0766795i | \(0.0244318\pi\) | ||||
−0.997056 | + | 0.0766795i | \(0.975568\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.5043 | − | 42.1493i | 0.773030 | − | 1.76081i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.799541 | −0.0333432 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4795 | −0.977464 | −0.488732 | − | 0.872434i | \(-0.662540\pi\) | ||||
−0.488732 | + | 0.872434i | \(0.662540\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.62697 | − | 10.5393i | 0.192291 | − | 0.438000i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.0313i | 0.789553i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.34293i | − | 0.0970342i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.0286 | + | 22.0918i | −0.993462 | + | 0.913382i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.81342 | −0.322494 | −0.161247 | − | 0.986914i | \(-0.551552\pi\) | ||||
−0.161247 | + | 0.986914i | \(0.551552\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.42951 | −0.141310 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.3417 | − | 10.6865i | −1.00128 | − | 0.439583i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.3770i | 1.04211i | 0.853524 | + | 0.521054i | \(0.174461\pi\) | ||||
−0.853524 | + | 0.521054i | \(0.825539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.1883i | 1.15561i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.93067 | + | 0.847602i | 0.0790172 | + | 0.0346900i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 47.1993 | 1.92851 | 0.964256 | − | 0.264971i | \(-0.0853623\pi\) | ||||
0.964256 | + | 0.264971i | \(0.0853623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6455 | 0.923728 | 0.461864 | − | 0.886951i | \(-0.347181\pi\) | ||||
0.461864 | + | 0.886951i | \(0.347181\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.7512 | + | 25.5143i | −1.13012 | + | 1.03902i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 7.95169i | − | 0.323282i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.4609i | − | 0.708717i | −0.935110 | − | 0.354359i | \(-0.884699\pi\) | ||
0.935110 | − | 0.354359i | \(-0.115301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.25550 | + | 11.9710i | −0.212964 | + | 0.485090i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.7308 | −1.28369 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2584 | −1.38368 | −0.691842 | − | 0.722049i | \(-0.743201\pi\) | ||||
−0.691842 | + | 0.722049i | \(0.743201\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.74960 | + | 6.26306i | −0.110875 | + | 0.252551i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.27244i | − | 0.0914851i | −0.998953 | − | 0.0457426i | \(-0.985435\pi\) | ||
0.998953 | − | 0.0457426i | \(-0.0145654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 29.5018i | − | 1.18578i | −0.805285 | − | 0.592889i | \(-0.797987\pi\) | ||
0.805285 | − | 0.592889i | \(-0.202013\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.91621 | + | 1.68251i | −0.197281 | + | 0.0675168i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.1547 | 1.12799 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.3630 | −0.814521 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.71576 | + | 1.63129i | 0.148393 | + | 0.0651473i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.48526i | 0.178839i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.10972i | − | 0.283034i | −0.989936 | − | 0.141517i | \(-0.954802\pi\) | ||
0.989936 | − | 0.141517i | \(-0.0451979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.3283 | + | 7.16845i | 0.648993 | + | 0.284920i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.7051 | 1.29786 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.8620 | −0.588855 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.1368 | + | 18.6392i | 0.677920 | + | 0.737356i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 11.6151i | − | 0.458769i | −0.973336 | − | 0.229384i | \(-0.926329\pi\) | ||
0.973336 | − | 0.229384i | \(-0.0736712\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.8165i | − | 1.17585i | −0.808916 | − | 0.587925i | \(-0.799945\pi\) | ||
0.808916 | − | 0.587925i | \(-0.200055\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.7537 | − | 31.3284i | 0.541553 | − | 1.23355i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.33222 | 0.0916892 | 0.0458446 | − | 0.998949i | \(-0.485402\pi\) | ||||
0.0458446 | + | 0.998949i | \(0.485402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.4699 | 1.51007 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.57363 | − | 12.6957i | 0.218448 | − | 0.497582i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 41.9909i | − | 1.64323i | −0.570042 | − | 0.821616i | \(-0.693073\pi\) | ||
0.570042 | − | 0.821616i | \(-0.306927\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 7.29642i | − | 0.285095i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.9612 | + | 19.5359i | 0.700732 | + | 0.762167i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.13706 | 0.278020 | 0.139010 | − | 0.990291i | \(-0.455608\pi\) | ||||
0.139010 | + | 0.990291i | \(0.455608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.2726 | −0.477347 | −0.238673 | − | 0.971100i | \(-0.576713\pi\) | ||||
−0.238673 | + | 0.971100i | \(0.576713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −56.5004 | − | 24.8048i | −2.19429 | − | 0.963337i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.68816i | − | 0.143021i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.68294i | 0.142604i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.0016 | − | 5.70795i | −0.502671 | − | 0.220682i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.90363 | 0.343721 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6271 | 0.756568 | 0.378284 | − | 0.925690i | \(-0.376514\pi\) | ||||
0.378284 | + | 0.925690i | \(0.376514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.93071 | − | 1.34524i | 0.151293 | − | 0.0517781i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.1834i | 1.04474i | 0.852717 | + | 0.522372i | \(0.174953\pi\) | ||||
−0.852717 | + | 0.522372i | \(0.825047\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 23.1303i | − | 0.887661i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3910 | + | 25.9464i | −0.436503 | + | 0.994269i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.4583 | 0.438439 | 0.219220 | − | 0.975676i | \(-0.429649\pi\) | ||||
0.219220 | + | 0.975676i | \(0.429649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4996 | −0.554001 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.8563 | + | 27.0064i | −0.452347 | + | 1.03036i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4.66127i | − | 0.177580i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 52.3164i | 1.99021i | 0.0988314 | + | 0.995104i | \(0.468490\pi\) | ||||
−0.0988314 | + | 0.995104i | \(0.531510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.0777 | + | 11.1041i | −0.458793 | + | 0.421811i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.5024 | −0.739768 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.9307 | −0.489786 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.05589 | − | 1.34160i | −0.115584 | − | 0.0507438i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 28.5063i | − | 1.07667i | −0.842731 | − | 0.538335i | \(-0.819054\pi\) | ||
0.842731 | − | 0.538335i | \(-0.180946\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.586852i | − | 0.0221335i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.4280 | − | 8.52924i | −0.731699 | − | 0.321230i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.8982 | −0.748349 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.18947 | 0.157339 | 0.0786694 | − | 0.996901i | \(-0.474933\pi\) | ||||
0.0786694 | + | 0.996901i | \(0.474933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.11338 | − | 6.53999i | 0.266772 | − | 0.245269i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.90588i | − | 0.146276i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.0325i | 1.08576i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.0220 | − | 22.8283i | 0.374280 | − | 0.852537i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.7537 | 0.736690 | 0.368345 | − | 0.929689i | \(-0.379924\pi\) | ||||
0.368345 | + | 0.929689i | \(0.379924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.25646 | 0.0840349 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.96615 | − | 15.8675i | 0.259074 | − | 0.590120i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 2.94466i | − | 0.109362i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10.7135i | − | 0.397342i | −0.980066 | − | 0.198671i | \(-0.936338\pi\) | ||
0.980066 | − | 0.198671i | \(-0.0636625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.3383 | − | 16.5432i | 0.790308 | − | 0.612709i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 64.6805 | 2.39230 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.3602 | −1.12138 | −0.560690 | − | 0.828026i | \(-0.689464\pi\) | ||||
−0.560690 | + | 0.828026i | \(0.689464\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.09962 | − | 3.99491i | −0.335645 | − | 0.147354i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.5303i | 1.23510i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.2449i | 0.450434i | 0.974309 | + | 0.225217i | \(0.0723091\pi\) | ||||
−0.974309 | + | 0.225217i | \(0.927691\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.39252 | + | 3.24546i | 0.271571 | + | 0.119225i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.9123 | 0.803885 | 0.401943 | − | 0.915665i | \(-0.368335\pi\) | ||||
0.401943 | + | 0.915665i | \(0.368335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.7079 | −0.941866 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.8544 | − | 20.5074i | −0.689845 | − | 0.750327i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 38.1565i | − | 1.39421i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.15169i | − | 0.115007i | −0.998345 | − | 0.0575034i | \(-0.981686\pi\) | ||
0.998345 | − | 0.0575034i | \(-0.0183140\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.1047 | − | 25.2944i | 0.404679 | − | 0.921779i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.4060 | −0.597076 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.2400 | −1.71697 | −0.858484 | − | 0.512840i | \(-0.828593\pi\) | ||||
−0.858484 | + | 0.512840i | \(0.828593\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.85788 | + | 4.23188i | −0.0674367 | + | 0.153608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.0033i | 1.81262i | 0.422617 | + | 0.906308i | \(0.361111\pi\) | ||||
−0.422617 | + | 0.906308i | \(0.638889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 25.0378i | − | 0.906431i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.9262 | − | 30.3746i | −1.00967 | − | 1.09820i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 76.5361 | 2.76356 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.3418 | 0.553241 | 0.276620 | − | 0.960979i | \(-0.410786\pi\) | ||||
0.276620 | + | 0.960979i | \(0.410786\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.3024 | − | 19.0106i | −1.55950 | − | 0.684649i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 6.44314i | − | 0.231744i | −0.993264 | − | 0.115872i | \(-0.963034\pi\) | ||
0.993264 | − | 0.115872i | \(-0.0369662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.12291i | 0.112178i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.17246 | + | 0.953751i | 0.0779365 | + | 0.0342156i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.69186 | 0.0606170 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.5208 | 0.805857 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.19657 | − | 18.1061i | −0.221447 | − | 0.647059i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.5992i | 1.02075i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.4072i | 1.61859i | 0.587400 | + | 0.809297i | \(0.300151\pi\) | ||||
−0.587400 | + | 0.809297i | \(0.699849\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.60748 | − | 10.4949i | 0.164031 | − | 0.373630i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.29683 | 0.259445 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.7138 | 0.629037 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.25295 | − | 2.85397i | 0.0444375 | − | 0.101220i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 48.8030i | − | 1.72869i | −0.502898 | − | 0.864346i | \(-0.667733\pi\) | ||
0.502898 | − | 0.864346i | \(-0.332267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 40.1110i | − | 1.41902i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.3383 | + | 27.8929i | −1.07195 | + | 0.985545i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.6042 | 0.832974 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.20046 | 0.148047 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.270852 | − | 0.118909i | −0.00953445 | − | 0.00418581i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.2338i | 1.66065i | 0.557278 | + | 0.830326i | \(0.311846\pi\) | ||||
−0.557278 | + | 0.830326i | \(0.688154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.45999i | − | 0.121497i | −0.998153 | − | 0.0607484i | \(-0.980651\pi\) | ||
0.998153 | − | 0.0607484i | \(-0.0193487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −45.9693 | − | 20.1814i | −1.61221 | − | 0.707792i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.898531 | 0.0314742 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.46281 | −0.296076 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.0286 | + | 22.0918i | −0.839628 | + | 0.771949i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.2740i | 0.951871i | 0.879480 | + | 0.475935i | \(0.157890\pi\) | ||||
−0.879480 | + | 0.475935i | \(0.842110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6650i | 0.824911i | 0.910978 | + | 0.412456i | \(0.135329\pi\) | ||||
−0.910978 | + | 0.412456i | \(0.864671\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.48545 | − | 3.38356i | 0.0517167 | − | 0.117801i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.8066 | −1.10602 | −0.553012 | − | 0.833173i | \(-0.686522\pi\) | ||||
−0.553012 | + | 0.833173i | \(0.686522\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.3070 | 1.15680 | 0.578400 | − | 0.815753i | \(-0.303677\pi\) | ||||
0.578400 | + | 0.815753i | \(0.303677\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.3689 | + | 30.4518i | −0.463763 | + | 1.05636i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 18.7871i | − | 0.650934i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 14.9219i | − | 0.516393i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.57167 | + | 19.2021i | 0.227150 | + | 0.663723i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.0337 | 0.933307 | 0.466653 | − | 0.884440i | \(-0.345460\pi\) | ||||
0.466653 | + | 0.884440i | \(0.345460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.4360 | 0.532275 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.6429 | − | 4.67244i | −0.366562 | − | 0.160928i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.1169i | 1.07045i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.95169i | − | 0.273223i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.2146 | + | 18.0940i | 1.41448 | + | 0.620984i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.668367 | 0.0229113 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.7698 | 1.15626 | 0.578129 | − | 0.815946i | \(-0.303783\pi\) | ||||
0.578129 | + | 0.815946i | \(0.303783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.65387 | + | 3.97422i | 0.124960 | + | 0.135915i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 27.6454i | − | 0.944350i | −0.881505 | − | 0.472175i | \(-0.843469\pi\) | ||
0.881505 | − | 0.472175i | \(-0.156531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.46667i | 0.0500421i | 0.999687 | + | 0.0250210i | \(0.00796528\pi\) | ||||
−0.999687 | + | 0.0250210i | \(0.992035\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.74960 | + | 6.26306i | −0.0937062 | + | 0.213444i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.2406 | −1.71021 | −0.855105 | − | 0.518454i | \(-0.826508\pi\) | ||||
−0.855105 | + | 0.518454i | \(0.826508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.4111 | 0.830003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.5193 | − | 44.4611i | 0.662910 | − | 1.50998i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.59472i | − | 0.291556i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 66.7088i | 2.26034i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.9153 | + | 24.9243i | 0.775564 | + | 0.843561i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.3607 | −0.823543 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.3367 | 0.855561 | 0.427780 | − | 0.903883i | \(-0.359296\pi\) | ||||
0.427780 | + | 0.903883i | \(0.359296\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.5701 | + | 5.07949i | 0.390249 | + | 0.171327i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.68919i | − | 0.124292i | −0.998067 | − | 0.0621460i | \(-0.980206\pi\) | ||
0.998067 | − | 0.0621460i | \(-0.0197945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 57.4928i | − | 1.93479i | −0.253279 | − | 0.967393i | \(-0.581509\pi\) | ||
0.253279 | − | 0.967393i | \(-0.418491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.8610 | + | 20.5729i | 1.57522 | + | 0.691550i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.3542 | 1.55642 | 0.778211 | − | 0.628003i | \(-0.216127\pi\) | ||||
0.778211 | + | 0.628003i | \(0.216127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.7051 | 1.09690 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.01354 | − | 23.9307i | 0.0674562 | − | 0.801710i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.24812i | 0.175622i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 44.2204i | − | 1.47813i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.69626 | + | 8.41936i | −0.123415 | + | 0.281114i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.3851 | 0.479770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.89231 | 0.196301 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.7537 | − | 31.3284i | 0.457696 | − | 1.04254i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.4325i | 1.31078i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 21.0235i | − | 0.698072i | −0.937109 | − | 0.349036i | \(-0.886509\pi\) | ||
0.937109 | − | 0.349036i | \(-0.113491\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.4415 | − | 19.7132i | 0.711170 | − | 0.653845i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.85784 | 0.293473 | 0.146737 | − | 0.989176i | \(-0.453123\pi\) | ||||
0.146737 | + | 0.989176i | \(0.453123\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.7780 | −0.820033 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.8457 | + | 4.76148i | 0.358548 | + | 0.157410i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.29642i | − | 0.240949i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.8152i | − | 0.917538i | −0.888556 | − | 0.458769i | \(-0.848291\pi\) | ||
0.888556 | − | 0.458769i | \(-0.151709\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.2449 | + | 17.2293i | 1.29316 | + | 0.567724i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.8052 | 1.47478 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.534387 | −0.0175705 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.43147 | + | 2.23548i | −0.0798599 | + | 0.0734227i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.5654i | 1.13405i | 0.823699 | + | 0.567027i | \(0.191907\pi\) | ||||
−0.823699 | + | 0.567027i | \(0.808093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.45810i | 0.0805611i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.3069 | + | 25.7549i | −0.370171 | + | 0.843177i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.7000 | −1.20022 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.5392 | 0.899665 | 0.449833 | − | 0.893113i | \(-0.351484\pi\) | ||||
0.449833 | + | 0.893113i | \(0.351484\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.6394 | + | 24.2344i | −0.347203 | + | 0.790860i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.6624i | 1.32556i | 0.748816 | + | 0.662778i | \(0.230623\pi\) | ||||
−0.748816 | + | 0.662778i | \(0.769377\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.92686i | 0.0627472i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.6504 | + | 7.06731i | −0.671756 | + | 0.229900i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.0057 | −0.422628 | −0.211314 | − | 0.977418i | \(-0.567774\pi\) | ||||
−0.211314 | + | 0.977418i | \(0.567774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.9607 | 1.52441 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.6142 | − | 11.2451i | −0.830596 | − | 0.364648i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 32.7687i | − | 1.06148i | −0.847534 | − | 0.530740i | \(-0.821914\pi\) | ||
0.847534 | − | 0.530740i | \(-0.178086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 54.4692i | − | 1.76258i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.5858 | − | 6.84244i | −0.503816 | − | 0.221185i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.4996 | −0.468216 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.7441 | 0.507875 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.8017 | + | 41.1159i | 1.21814 | + | 1.32494i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 13.6199i | − | 0.438440i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.8479i | 1.76379i | 0.471445 | + | 0.881895i | \(0.343733\pi\) | ||||
−0.471445 | + | 0.881895i | \(0.656267\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.10258 | + | 9.34489i | −0.131794 | + | 0.300201i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.80543 | −0.314671 | −0.157336 | − | 0.987545i | \(-0.550290\pi\) | ||||
−0.157336 | + | 0.987545i | \(0.550290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.5024 | −0.625218 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.95531 | − | 6.73162i | 0.0946457 | − | 0.215585i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.64150i | 0.212480i | 0.994340 | + | 0.106240i | \(0.0338812\pi\) | ||||
−0.994340 | + | 0.106240i | \(0.966119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.6562i | 1.17154i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.8050 | + | 26.9798i | 0.791963 | + | 0.861398i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.70906 | 0.213986 | 0.106993 | − | 0.994260i | \(-0.465878\pi\) | ||||
0.106993 | + | 0.994260i | \(0.465878\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.4566 | −1.00229 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.4280 | − | 8.52924i | −0.618399 | − | 0.271489i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 9.63831i | − | 0.306481i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 0.245286i | − | 0.00779177i | −0.999992 | − | 0.00389588i | \(-0.998760\pi\) | ||
0.999992 | − | 0.00389588i | \(-0.00124010\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −56.2686 | − | 24.7030i | −1.78563 | − | 0.783925i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.49499 | 0.0790965 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.6977 | 0.940537 | 0.470269 | − | 0.882523i | \(-0.344157\pi\) | ||||
0.470269 | + | 0.882523i | \(0.344157\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.28584 | + | 1.12453i | −0.103959 | + | 0.0355787i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1104.2.e.f.47.4 | yes | 8 | |
3.2 | odd | 2 | 1104.2.e.g.47.6 | yes | 8 | ||
4.3 | odd | 2 | 1104.2.e.g.47.5 | yes | 8 | ||
12.11 | even | 2 | inner | 1104.2.e.f.47.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1104.2.e.f.47.3 | ✓ | 8 | 12.11 | even | 2 | inner | |
1104.2.e.f.47.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1104.2.e.g.47.5 | yes | 8 | 4.3 | odd | 2 | ||
1104.2.e.g.47.6 | yes | 8 | 3.2 | odd | 2 |